A Problem with Distance Variables and Alternatives for Their Use

Abstract

Researchers commonly use distance variables to: (i) estimate the direct influence of a landmark on an outcome of interest, such as a neighborhood park on home price; or (ii) control for omitted spatial influences that affect predictions of key policy variables. While both uses continue, the use of distance as a control, such as distance to Central Business District (CBD), is now more common. Using distance to a given position such as CBD is added to multivariate analysis as a method to capture all remaining, or omitted spatial effects that influence the dependent variable. We show that there is a latent and inherent identification problem with the distance variable; and we show that this extends to the use of distance as a control. These biases affect more than the distance variable. They generate inconsistent estimates for all other spatially distributed variables in a model. We then introduce an alternative control that captures unmodeled influences that vary across space, and we show that this fully stabilizes all model parameter estimates and measures of model efficiency.